The compdata package

Based on Wouter Swierstra's Functional Pearl Data types à la carte
(Journal of Functional Programming, 18(4):423-436, 2008),
this package provides a framework for defining recursive
data types in a compositional manner. The fundamental idea of
compositional data types is to separate the signature of a data type
from the fixed point construction that produces its recursive
structure. By allowing to compose and decompose signatures,
compositional data types enable to combine data types in a flexible
way. The key point of Wouter Swierstra's original work is to define
functions on compositional data types in a compositional manner as
well by leveraging Haskell's type class machinery.

Building on that foundation, this library provides additional
extensions and (run-time) optimisations which make compositional data types
usable for practical implementations. In particular, it
provides an excellent framework for manipulating and analysing
abstract syntax trees in a type-safe manner. Thus, it is perfectly
suited for programming language implementations, especially, in an environment
consisting of a family of tightly interwoven domain-specific languages.

Modular definition of functions on compositional data types through
catamorphisms and anamorphisms as well as more structured
recursion schemes such as primitive recursion and co-recursion,
and course-of-value iteration and co-iteration.

Support for monadic computations via monadic variants of all
recursion schemes.

Support of a succinct programming style over compositional data types
via generic programming combinators that allow various forms of
generic transformations and generic queries.

Generalisation of compositional data types (terms) to
compositional data types "with holes" (contexts). This allows
flexible reuse of a wide variety of catamorphisms (called
term homomorphisms) as well as an efficient composition of them.

Operations on signatures, for example, to add and remove
annotations of abstract syntax trees. This includes combinators to
propagate annotations fully automatically through certain
term homomorphisms.

Optimisation of the implementation of recursion schemes. This
includes short-cut fusion style optimisation rules which yield a
performance boost of up to factor six.

Automatic derivation of instances of all relevant type classes for
using compositional data types via Template Haskell. This includes
instances of Prelude.Eq, Prelude.Ord and Prelude.Show that are
derived via instances for functorial variants of them. Additionally,
also smart constructors, which allow to easily construct inhabitants
of compositional data types, are automatically generated.

Mutually recursive data types and
generalised algebraic data types (GADTs). All of the above is also lifted
to families of mutually recursive data types and (more generally) GADTs.
This extension resides in the module Data.Comp.Multi.

Parametric compositional data types. All of the above is also lifted
to parametric data types, which enables support for parametric higher-order
abstract syntax (PHOAS). This extension resides in the module
Data.Comp.Param.

Generalised parametric compositional data types. All of the above is also
lifted to generalised parametric data types, which enables support for
typed parametric higher-order abstract syntax (PHOAS). This extension
resides in the module Data.Comp.MultiParam.

Examples of using (generalised) (parametric) compositional data types are
bundled with the package in the libray examples.